I just moved to New Paltz at the beginning of the year, but up until then I was a member at both BKB and The Cliffs, I've spent time at all three of The Cliffs, BKB OG, and BKB QB. My take:
BKB has the best bouldering and the routesetting on lead/toprope, while inconsistent, can be better at times. I get the feeling that one or two of the setters are really good, and some others are maybe inexperienced (which will probably improve over time). That said, as a rope climber, they're simply too hampered by a lack of space in both gyms, especially for lead. TR is worthwhile in both BKB gyms, but if you're interested in leading, I wouldn't bother. They also make a lot of decisions I wouldn't, basically choosing a hip aesthetic over what would contribute to the best climbing. The new walls they put in at OG are a good example: they look great, but they don't have any texture and generally don't act like rock at all. BKB also does a lot of events, which are probably great if you participate in them, but if you're like me and just want to climb, they often get in the way.
The Cliffs leading is excellent. They have taller walls, more variety of routes, and better leading in general.
Both gyms have decent weightlifting/hangboarding/etc. areas. I'd go to BKB OG for weights/hangboarding, BKB QB for yoga/stretching area, but the Cliffs is adequate in both these areas.
BKB QB has a wooden crack machine and saunas, if either one of those are your thing. The Cliffs has cracks as well, but they're the Walltopia style ones, which I personally don't love.
If I had to choose one gym, I'd honestly probably choose The Cliffs, but that's more a reflection of what I want in a gym. I'm mostly into leading and I don't care about most events, so I get the most out of having a big gym with lots of leading options. YMMV.
Other gyms to check out: Chelsea Piers, Steep Rock. I've heard good things about the leading at Chelsea Piers, and Steep Rock, while purely bouldering, is very good for bouldering.
Also, there's rumors of a MetroRock opening in Bushwick. I have no idea if the rumors are true.
Finally, be sure to get the NYC Bouldering guide, there's plenty of free bouldering in Central Park: I recommend Worthless Boulder at the north end as my favorite. And hit me up if you ever want to climb in the Gunks.